Problem: Michael is 27 years older than Stephanie. Ten years ago, Michael was 4 times as old as Stephanie. How old is Stephanie now?
Solution: We can use the given information to write down two equations that describe the ages of Michael and Stephanie. Let Michael's current age be $m$ and Stephanie's current age be $s$ The information in the first sentence can be expressed in the following equation: $m = s + 27$ Ten years ago, Michael was $m - 10$ years old, and Stephanie was $s - 10$ years old. The information in the second sentence can be expressed in the following equation: $m - 10 = 4(s - 10)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $s$ , it might be easiest to use our first equation for $m$ and substitute it into our second equation. Our first equation is: $m = s + 27$ . Substituting this into our second equation, we get the equation: $(s + 27)$ $-$ $10 = 4(s - 10)$ which combines the information about $s$ from both of our original equations. Simplifying both sides of this equation, we get: $s + 17 = 4 s - 40$ Solving for $s$ , we get: $3 s = 57$ $s = 19$.